Download 1 Dark Matter as a consequence of electric charge non

Dark Matter as a consequence of electric charge non-conservation will it remain “dark” forever?
Richard M. Weiner
Laboratoire de Physique Théorique, Univ. Paris-Sud, Orsay, France and
Physics Department, University of Marburg, Germanyx)
It is conjectured that dark matter (DM) was produced before inflation from neutral particles
present after the Big Bang and survived inflation due to a specific coupling with gravitation,
while the charged particles existing after the Big Bang disappeared during inflation in a
process of charge non-conservation. Ordinary matter was produced at a later stage at a lower
temperature following a symmetry restoring phase transition. In this way the non-luminous
character of dark matter and the existence of two types of matter, ordinary and dark, get a
natural explanation. Because of the high temperatures preceding inflation, the masses of
particles produced during that time are too large to be detected by conventional particle
physics methods and possibly will never be detected.
Dark Matter (DM) constitutes one of the most challenging, unsolved problems of
cosmology and of physics in general (for more recent reviews cf. e.g. refs. [1]): although it
is responsible for about 85% of the total mass density of the Universe, the mechanism of
its creation, its constituents and the reason for its main property, its darkness, are unknown.
At present the most popular attempts of explanations of DM are based on the assumption
that its constituents are weakly interacting massive particles (WIMP -s), which are
electrically neutral. However why these constituents have not been detected in the
laboratory, despite the fact that other types of neutral weakly interacting particles like
neutrinos have been, is unknown. Moreover within the presently accepted lore of
cosmology - the Big Bang followed by inflation and then by standard model physics - the
question which is at the heart of the dark matter mystery “why does the Universe contain
two types of matter, one ‘ordinary’ and accessible to optical devices and another one,
‘dark’, remains unanswered. In other words, is the existence of two types of matter, one
dark and one ordinary, a natural consequence of the evolution of the Universe, as we
believe to know it at present?
x)
Email address: [email protected]
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One of the aims of this note is to suggest a positive answer to this question and to
show that the creation of dark matter might cease to be a mystery once we give up the
assumption, made so far in all approaches to DM, that one of the laws of physics, that
of conservation of electric charge, which is valid in our universe at present, was also
valid immediately after the Big Bang. In particular we assume that dark matter was
produced as a consequence of the fact that the charged particles created immediately
after the Big Bang lost their electric charge during inflation. Charge conservation was
established at a later stage. This assumption is also used to explain why DM has not
yet been “seen” and to suggest that it possibly will never be.
We start by considering the Universe after the Big Bang. What appears quite well
established is the fact that it underwent a period of inflation.
Without losing generality it can be assumed that before this happened it consisted of
charged and neutral particles. In accordance with what is known at present about
inflation charged particles disappeared during inflation. This observation due initially
to Guth [2] has remained unchallenged by the subsequent formulations of inflation.
From the point of view of the early Universe this represents a process of global
charge non-conservation. On top of that we assume that due to a specific coupling
with the gravitational field to be described below neutral particles survived inflation.
These “early” neutral particles constitute what appears at present dark matter. For the
sake of concreteness (cf. below) we will assume that these particles are thermal relics.
Ordinary matter was produced after inflation in a charge symmetry restoring phase
transition and consists of charged and “late” neutral particles, which besides the
absence of the specific gravitational coupling mentioned above, differ from the
“early” ones, among other things, by their mass.
This explanation of the existence of dark and ordinary matter constitutes in a certain
sense a modest attempt to follow Einstein’s advice to try to “understand not only how
nature works, but to understand why nature is the way it is”.
Since according to our main postulate dark matter is produced before inflation which
takes place at a temperature
TDM ~ Tinfl ≈ 10-3-10-4 MPlanck ,
(1)
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the average mass MDM of its constituents is by orders of magnitude larger than that of
ordinary matter Mord, which were produced later at temperatures
Tord < Tinfl .
(2)
This is the reason why DM constituents have not been detected experimentally in the
laboratory, either in accelerator or in cosmic rays physics.
That the assumption of charge non-conservation is not so shocking as it might appear
at a first look can be realized by reminding that charge conservation, like most other
conservation laws, is, according to Noether’s theorem, a consequence of a symmetry
of the Lagrangian, in this case the electromagnetic gauge symmetry. On the other
hand, whether a given solution of the equations of motion of a Lagrangian exhibits a
given symmetry or not depends on external circumstances like temperature, matter
densities or external fields and on details of the Lagrangian. In particular, the fact that
most known symmetries are conserved at high temperatures led by analogy to the
assumption that this is also valid for the very early periods of the evolution of the
Universe, so that most conservation laws known at present were also valid
immediately after the Big Bang.
However ferromagnets like the Rochelle salt are a well known counter example of the
observation that high temperatures lead to more symmetry [3]. What is even more
relevant for the present approach is the fact that for global symmetries the breaking of
symmetry at high temperatures is quite a general phenomenon, with possible
implications for the early stages of the Universe expansion [4]. Actually
non- conservation of electric charge at high temperatures was proposed already
a long time ago [5] in order to explain the absence of magnetic monopoles.
Similarly the assumption of symmetry violation at high temperatures was used to
explain baryogenesis [6].
In the present approach we assume that the gauge symmetry associated with
electric charge was spontaneously broken after the Big Bang and subsequently
restored at lower temperatures, during the expansion of the Universe [7]. That
happened through a phase transition at a critical temperature Tcrit ≥ Tord.
This assumption shifts the DM creation to the very early stages of the
Universe evolution, when gravitational effects are still important. And
although the quantum field theory of gravitation is non-renormalizable, almost
everything we know today about the beginning of the Universe is based, besides the
theory of general relativity, on classical gravitation. We assume that this applies also
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for the following considerations, the more so that quantum effects are most probably
not important at high temperatures [8].
The question then arises how dark matter created before inflation survived the
exponential expansion characteristic for inflation, which is expected to wash out any
conserved quantity. Here gravitation comes into play through the “mimetic”
mechanism of Chamseddine and Mukhanov [9], who described dark matter by a
scalar field Φ coupled to the inflaton field φ through a term of the form ΦF(φ), where
F is a slow function of φ.
These authors prove that at the end of the exponential expansion representing
inflation
a ≡ H –1 exp (Ht),
(3)
where a defines the flat metric
ds2 = dt2 - a2 (t) δikdxidxk,
(4)
and H is the Hubble constant, the diference between the trace G of the Einstein tensor
Gµν = Rµν - ½Rgµν and the trace T of the energy momentum tensor of matter Tµν can
be approximated by
G – T ≈ - F(φ)/3H ≠ 0,
(5)
which means that dark matter as defined above survives inflation.
Further development of this approach might include e.g. the use of the
experimentally observed relic density of dark matter in the determination of yet
unknown aspects and parameters of the mimetic formalism, a topic of current interest
(cf. e.g.[10]).
To summarize: the existence of dark matter can be considered as a consequence of
the breakdown in the early stages of Universe expansion of a fundamental principle
of particle physics, electric charge conservation. This conclusion emerges
independently of any more detailed quantitative considerations.
The existence of particles with masses up to the inflation temperature Tinfl could
contribute to solving the hierarchy problem, i.e. filling the gap between the Higgs
mass characteristic for the electroweak interaction and the Planck mass characteristic
for gravitation.
The most far reaching experimental consequence of the above considerations is the fact that
because of the high mass of its constituents dark matter may remain “dark” forever in the
sense that its constituents will never be observed in the laboratory, although it represents one
of the strongest signals of the early Universe.
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Acknowledgements: The continuous advice and interest of Masud Chaichian
in this work is gratefully acknowledged. I am also much indebted to
Maxim Khlopov for important suggestions, to Paul Langacker, Markku
Oksanen and Cristian Armendariz-Picon for instructive observations and to
Tom Kibble and Archil Kobakhidze for encouraging comments.
References
[1] Maxim Khlopov, Int. J. Mod. Phys. A 28 (2013), 495; Kalliopi Petraki, Raymond
R. Volkas, Int. J. Mod. Phys. A 28, (2013) 1330028.
[2] Alan H. Guth, Phys. Rev. D23 (1981) 347).
[3] Cf. e.g. L. D. Landau, E. M. Lifshitz, Statistical Physics, Elsevier ButterworthHeinemann, ISBN-13: 978-0750633727. In particle physics the breaking of symmetries
with increasing temperatures was discussed by S. Weinberg, Phys. Rev. D9
(1974) 3357, Mohapatra, R.N.and Senjanovic, G., Phys. Rev.Lett 42, (1979)
1651, Phys. Rev. D20, (1979) 3390 and Phys. Lett. 89B, (1979) 57.
[4] Goran Senjanovic, http://lanl.arxiv.org/abs/hep-ph/9805361.
[5] Paul Langacker and So-Young Pi, Phys. Rev. Lett. 45 (1980) 1.
[6] Scott Dodelson and Lawrence M. Widow, Phys. Rev. Lett. 64 (1990) 340;
Phys. Rev. D42 (1990) 326; Modern Physics Letters A (1990) 1623.
[7] The fact that the violation of local gauge invariance induces the violation of
global invariance is due to the spontaneous nature of the breaking of the local
invariance. For a more detailed analysis of this issue cf. G. S. Guralnik, C. R.
Hagen, and T.W. B. Kibble, Phys. Rev. Lett. 13 (1964) 585.
[8] Cf. e.g. J. Zinn-Justin, Saclay Lecture Notes, arXiv-hep-ph/0005272.
[9] Ali H. Chamseddine, Viatcheslav Mukhanov, JHEP 1311 (2013) 135.
[10] Ali H. Chamseddine, Viatcheslav Mukhanov, Alexander Vikman,
Journal of Cosmology and Astroparticle Physics, 06 (2014) 017;
Masud Chaichian, Josef Kluson, Markku Oksanen, Anca Tureanu, JHEP 12 (2014) 102;
V. K. Oikonomu, http://lanl.arxiv.org/abs/1609.03156.
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